Lambeck and Hopgood (1981, 1982) have made a comparative study of spectral characteristics of the angular momentum of atmospheric circulation and fluctuations in the Length-of-Day (LOD) data. The Fourier analysis of these data reveals a good correlation between the two processes, including a large spread of power in the range of a 20- to 70-month period. We re-examine here the above two time series by using the Walsh spectral analysis, which seems to be more appropriate for series with sharp peaks and reversals. The comparative study shows that in addition to 12-, 6- and 3-month seasonal terms, the present work discovers statistically significant (90% confidence interval) periods of (i) 26 months (hitherto weakly resolved) associated with a quasibiennial term, and (ii) 40 ± 4 months in both the data. The resolution of the spread components removes meteorological noise uncertainity from astronomical observations of LOD in the study of the excitation mechanism of solid earth.